Such a shaving apparatus is known, for example, from U.S. Pat. No. 2,120,009. In this shaving apparatus the opposite member is formed by a rotatably drivable cylinder having spiral-like extending grooves. During operation of the apparatus the skin to be shaved engages a part of the circumference of the cylinder. The danger exists that as a result of the friction the skin is taken along by the cylinder and is urged against the cutting member so that injuries may be the result.